Reflectionless Boundary Propagation Formulas for Partial Wave Solutions to the Wave Equation




Navarro, Jaime
Warchall, Henry A.

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Southwest Texas State University, Department of Mathematics


We consider solutions to the wave equation in 3+1 spacetime dimen- sions whose data is compactly supported at some initial time. For points outside a ball containing the initial support, we develop an outgoing wave condition, and associated one-way propagation formula, for the partial waves in the spherical-harmonic decomposition of the solution. The prop- agation formula expresses the l-th partial wave at time t and radius a in terms of order-l radial derivatives of the partial wave at time t − ∆t and radius a − ∆t. The boundary propagation formula can be applied to any differential equation that is well-approximated by the wave equation outside a fixed ball.



One-sided wave propagation, Wave equation, Reflectionless boundary conditions, Partial waves, Spherical-harmonic decomposition, Open-space boundary conditions


Navarro, J. & Warchall, H. A. (1995). Reflectionless boundary propagation formulas for partial wave solutions to the wave equation. <i>Electronic Journal of Differential Equations, 1995</i>(17), pp. 1-14.


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